To develop a high performance MHD numerical simulation method is an important factor in research of numerical prediction of space weather. The upwind flux splitting scheme based on finite volume method has good ability to capture discontinuities. Steger-Warming and AUSM (Advection Upstream Splitting Method) schemes are two outstanding upwind flux splitting scheme, which are classified as FVS (Flux Vector Splitting) method. In this paper, these two schemes are applied to solve the Extended Generalized Lagrange Multiplier Magnetohydrodynamics (EGLM-MHD) equation with Galilean invariance. Results obtained from Orszag-Tang vortex and three-dimensional blastwave problem indicate that those two schemes are both robust and accurate. Particularly, AUSM scheme is superior to Steger-Warming scheme in divergence error control and computational speed.
